Gauge invariance in fractional field theories

author:
R. Herrmann
abstract:
The principle of local gauge invariance is applied to fractional wave equations and the interaction term is determined up to order $o(\bar{g})$ in the coupling constant $\bar{g}$. As a first application, based on the Riemann-Liouville fractional derivative definition, the fractional Zeeman effect is used to reproduce the baryon spectrum accurately.
The transformation properties of the non relativistic fractional Schrödinger-equation under spatial rotations are investigated and an internal fractional spin is deduced.